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Lesson Plan #008
Date: Thursday September 18th, 2014
Class: Geometry
Topic: Using if…then… statements in logic
Aim: How do we use if…then… statements in logic?
HW #008: Page 647 #’s 1-10
Objectives:
1) Students will be able to use if…then… statements in logic.
Do Now:
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3)
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PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
In mathematics, you will come across many
if… then… statements.
For example,
“If a number is even, then it is
divisible by two”.
In logic, a conditional is a compound sentence usually formed by using the words if…then to combine
two simple sentences. When p and q represent simple sentences, the conditional if p then q is written in symbols as p  q .
A conditional is sometimes called an implication. Thus, we may also read the symbols for the conditional p  q as
p implies q .
Conditional statements have two parts. The part following
The part following
if
is the hypothesis or the antecedent.
then is the conclusion or the consequent.
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Medial Summary:
A conditional statement, symbolized by p
q, is an if-then statement in which p is
a hypothesis and q is a conclusion. The logical connector in a conditional statement is denoted by
the symbol
. The conditional is defined to be true unless a true hypothesis leads to a false
conclusion. A truth table for p
q is shown.
Exercises:
1) Which of the following is a conditional statement?
A) Amy plays soccer or Bill plays hockey.
B) Bill plays hockey when Amy plays soccer.
C) If Amy plays soccer then Bill plays hockey.
D) None of the above.
2) Given:
r: You give me twenty dollars.
s: I will be your best friend.
Problem:
Which of the following statements represents, "If you give me twenty dollars, then I will be your best friend"?
A) r  s
B) r  s
C) s  r
D) None of the other choices
3) What is the truth value of
A) True
B) False
4) Given:
a: x is
b: x is
Problem:
A) True
r  s when the hypothesis is false and the conclusion is true in Example 2?
C) Not enough information was given.
prime.
odd.
What is the truth value of a  b when x = 2?
B)False
C) Not enough information was given
5) What is the truth value of a  b when x = 9 in Exercise 4?
A) True
B) False
C) Not enough information was given
6) Tell whether the sentence is true false or open.
If 1  2  3 then 2  3  4
Definition: A biconditional statement is defined to be true
whenever both parts have the same truth value.
The biconditional operator is denoted by a
double-headed arrow
. The biconditional p
q represents "p if and only if q," where p is a
hypothesis and q is a conclusion. The following is
a truth table for biconditional p q.
D)None of the above.
D) None of the other choices
D) None of the above.
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Mathematicians abbreviate "if and only if" with "iff."
Exercises
1. Given:
a: y - 6 = 9
b: y = 15
Problem:
The biconditional a  b represents which of the following sentences?
A) If y - 6 = 9, then y = 15.
B) y - 6 = 9 if and only if y = 15.
C) If y = 15, then y - 6 = 9.
D) None of the above.
2.
Given:
r: 11 is prime.
s: 11 is odd.
Problem:
The biconditional r  s represents which of the following sentences?
A) If 11 is prime, then 11 is odd.
B) If 11 is odd, then 11 is prime.
C) 11 is prime iff 11 is odd.
D) None of the above.
3. Given:
x y
yx
Problem:
If both of these statements are true then which of the following must also true?
A) x  y  y  x
B) x  y
C) x iff y
D) All of the other choices

 

4. Given:
m  n is biconditional
Problem:
Which of the following is a true statement?
A) m is the hypothesis
B) m is the conclusion
D) n is a biconditional statement
C) n is a conditional statement
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